Ch. 9 examples

9.1/ 9.2: Test on a single population mean Intro: So far our work has been on estimation, or confidence intervals Now the focus is on Hypothesis Testing

Types of Hypotheses The null hypothesis H0 is one which expresses the current state of nature of belief about a population The alternative (or research) hypothesis (H 1 or H a ) is one which reflects the researcher’s belief. (It will always disagree with the null hypothesis). Note: the alternative hypothesis can be one or two tailed.

Level of significance Generally, this value is .05, .10, or .01

Type I and Type II error

Analogy- Courtroom Reality Defendant is innocent Defendant is guilty   Reality Defendant is innocent Defendant is guilty Conclusion (Sentence) Not Guilty Acquittal-                   Correct conclusion Error Guilty Conviction-                   

Step 1 and 2: H 0 and H 1 We have a 7 step process to follow (template available on the webpage) The first two steps cover defining the two hypotheses Determining these correctly is important, but it can be tricky. So let’s consider some examples

Should you use a 2 tail, or a right, or left tail test? 2-tailed ex H0: µ= __ H1: µ ≠ __ Left tail ex H0: µ = ___ H1: µ < ___ Right tail ex H0: µ = __ H1: µ > __ Test whether the average in the bag of numbers is or isn’t 100. Test if a drug had any effect on heart rate. Test if a tutor helped the class do better on the next test. Test if a drug improved elevated cholesterol.

Ex: Left tail test- cholesterol A group has a mean cholesterol of 220. The data is normally distributed with σ= 15 After a new drug is used, test the claim that it lowers cholesterol.

Ex - right tail- tutor Scores in a MATH117 class have been normally distributed, with a mean of 60 all semester. The teacher believes that a tutor would help. After a few weeks with the tutor, a sample of 35 students’ scores is taken. The sample mean is now 62. Assume a population standard deviation of 5. Has the tutor had a positive effect?

Summary of Hypothesis test steps Hypothesis Testing Template Step 1: State the null hypothesis (in words and in symbols) - Step 2: State the alternative hypothesis (in words and in symbols) - Step 3: State the test statistic (and check assumptions!) - Step 4: Find the critical (rejection) region - Step 5: Compute the test statistic - Step 6: Make a decision - Must be of the form: (Reject H0 –or– Do Not Reject H0) at the  = ____ level. Then explain the implication of this decision in terms of the original problem. Step 7: Find the p-value (when appropriate) - and interpret this p-value – If p value < , we reject H0 at the  level If p value > , we do not reject H0 at the  level.

Do Ex 1 and 2 on handout

When  is unknown… … we use the t distribution and use s as an estimate for 

Critical values for t Find the CV for one tail examples when:

Do Ex 3 on handout

Notes Hypothesis Template is posted on webpage HW is from the BOOK (not Webassign) Section 9.2: 7, 9, 11, 17, 19 On these, do the 7-part method, ignoring the exact wording of the problem Solutions are on the course web page Next is NOT next week. It will be delayed another week.